Refrac efficiency monitoring

ABSTRACT

A method of treatment of a subterranean formation penetrated by a wellbore, where the well has a plurality of previously stimulated intervals includes: a) pumping a viscous pill into a well with pressure curve registration by a wellhead pressure sensor; b) determining a depth (L) of treatment fluid entry point and depth uncertainties (L); c) generating a water hammer at the wellhead which excites tube waves; d) determining the depth (L) of the treatment fluid entry point and the depth uncertainties (L) by processing a water hammer by high frequency pressure monitoring method; e) determining a tube wave velocity from a combination of data from (b) to (d); f) performing a fracturing treatment; and g) generating a water hammer at the wellhead at the end of the fracturing treatment (f) with refined depth of treatment fluid entry point and with lower uncertainty.

BACKGROUND

Hydrocarbons (oil, natural gas, etc.) are obtained from a subterranean geologic formation (i.e., a “reservoir”) by drilling a wellbore that penetrates the hydrocarbon-bearing formation. This provides a partial flowpath for the hydrocarbon to reach the surface. In order for the hydrocarbon to be “produced,” that is travel from the formation to the wellbore (and ultimately to the surface), there is a sufficiently unimpeded flowpath from the formation to the wellbore.

Fractures in earth formations are of major significance in the production of subsurface fluid resources such as hydrocarbons. In formations of low permeability and low porosity, the potential production from a borehole into the formation is directly related to the number of open fractures. Secondary recovery of hydrocarbons after production by the formation's inherent fluid pressure has been exhausted often involves the injection of fluids to move hydrocarbons towards a producing well, and knowledge of the fractures in the formation is valuable in predicting the overall recovery.

Hydraulic fracturing is the method of well stimulation by generating fractures inside hydrocarbon-bearing formation in which fractures are created by means of pumping fluid and propping agent downhole at high pressure. The main objective of fracturing is to increase well productivity and fracturing and acidizing jobs to increase formation permeability may be designed based on reservoir data, proppant, acid volume to be pumped, target productivity index of the well, and the like. However, the difficulty in characterizing the effectiveness of a hydraulic fracturing treatment can introduce a certain degree of uncertainty as to the total amount of hydrocarbon recoverable from a given reservoir.

SUMMARY

This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter.

In one aspect, embodiments disclosed herein relate to a method of treatment of a subterranean formation penetrated by a wellbore, where the well has a plurality of previously stimulated intervals includes: a) pumping a viscous pill into a well with pressure curve registration by a wellhead pressure sensor; b) determining a depth (L) of treatment fluid entry point and depth uncertainties (ΔL); c) generating a water hammer at the wellhead which excites tube waves; d) determining the depth (L) of the treatment fluid entry point and the depth uncertainties (ΔL) by processing a water hammer by high frequency pressure monitoring method; e) determining a tube wave velocity from a combination of data from (b) to (d); 0 performing a fracturing treatment; and g) generating a water hammer at the wellhead at the end of the fracturing treatment (f) with refined depth of treatment fluid entry point and with lower uncertainty.

Other aspects and advantages of the claimed subject matter will be apparent from the following description and the appended claims.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows variation of pressure versus time in accordance with embodiments of the present disclosure.

FIG. 2 shows a cepstrogram in accordance with embodiments of the present disclosure.

FIG. 3 is a flow diagram illustrating a treatment in accordance with embodiments of the present disclosure.

FIG. 4 depicts the variation of pressure versus time for viscous pill pumping in accordance with embodiments of the present disclosure.

FIGS. 5 and 6 are graphical representations illustrating refracturing monitoring processes in accordance with embodiments of the present disclosure.

DETAILED DESCRIPTION

Generally, embodiments disclosed herein relate to methods of monitoring refracturing effectiveness of previously stimulated subterranean formations to improve well performance and recovery of hydrocarbons. More specifically, embodiments disclosed herein relate to methods for monitoring, controlling, evaluating and improving the refracturing effectiveness in a well with multiple previously stimulated stages. In some embodiments, methods may also include performing one or more remediation actions to modify a treatment design in real-time. The inventors of the present disclosure have discovered that using the viscous pill technology combined with high frequency pressure measurement with water hammer generation may provide real-time information regarding the refracturing effectiveness of a subterranean formation with higher accuracy and robustness and lower price and within shorter period of time than when only one of the technologies is used. The higher accuracy of the refracturing effectiveness achieved as described herein may allow for restimulation of more stages (than with the use of viscous pill technology only for example) with the minimal risk of understimulation of some stages and overstimulation of others.

As defined herein, understimulation may be understood as hydraulic or acid fracturing. Furthermore, as defined herein, the term “stage” or “interval” defines an element of wellbore completion that enables the possibility of performing a fracturing operation (treatment) in this place. In addition, a multistage treatment (a multistage frac) is defined as the consecutive (stage-by-stage) fracturing operations. All these definitions may be found in the Schlumberger Oilfield Glossary.

Methods in accordance with the present disclosure may be used to monitor the effectiveness of refracturing treatments in a well that has a plurality of previously stimulated stages. Such methods may be applied for monitoring the effectiveness of a secondary or a tertiary stimulation treatment with the purpose of providing real-time information regarding the refracturing effectiveness of each stage stimulation. Such information may help an operator to make a decision, such as whether the given production stage is already effectively stimulated or whether isolation of other stages should be performed with the further restimulation of a given stage.

According to the present embodiments, the method of monitoring refracturing effectiveness combines viscous pill (VP) technology, i.e. pumping of a marker viscous fluid (with a high viscosity, degradable with time) and high frequency pressure measurement (HFPM) with water hammers generation at the end of the treatment stage and their further processing.

In practice, the viscous pill technology may allow for identification of a position of a fracture produced during a hydraulic fracturing stimulation of a formation. Such a method is based on the local change of the viscosity and/or density of the liquid being pumped into the well and includes pumping a fracturing fluid into the wellbore at a pressure above the fracture pressure of the formation to create at least one fracture. Afterwards, a marker pulse is pumped into the well, followed by pumping fracturing fluid back into the well. At the entrance of the marker pulse to at least one of the hydraulic fractures, a pressure detectable response is observed, and the position of the fracture is determined by the volume of fracturing fluid injected after the marker pulse. The marker pulse is a portion of a liquid exhibiting different viscosity and/or density of the fracturing fluids injected before and after the marker pulse. Examples of viscous pill technology are discussed in greater detail in WO Publication No. 2018/004370A1.

As noted above, the viscous pill technology may be combined with high frequency pressure measurement (HFPM) with water hammers generation. In one or more embodiments, the high frequency pressure measurement (HFPM) may involve a cepstrum analysis. For example, WO Publication No. 2018/004369A1 discusses in greater detail a method of monitoring the well operations based on cepstrum analysis of downhole pressure data recorded at the wellhead. The method is designed to locate a downhole object which reflects a hydraulic signal. According to such a method, a well is filled with a fluid medium that permits the passage of a hydraulic signal. A hydraulic signal source is provided, which is in communication with the well via the fluid medium and is designed to generate a hydraulic signal. A pressure transmitter is designed to register the hydraulic signal and is in communication via the fluid medium, with the well and with at least one hydraulic signal source. A hydraulic signal is registered using a pressure sensor, and a pressure cepstrogram is generated, highlighting an intense signal on the pressure cepstrogram. Afterwards, the object which reflects the hydraulic signal is located.

According to one or more embodiments, the method of treatment of a subterranean formation penetrated by a wellbore, such as a refracturing monitoring method, involves the use of sequential viscous pill pumping (and depth determination), high frequency pressure monitoring of water hammers (at the end of viscous pill also for depth determination) and diverter to plug the stages with the highest fluid acceptance, with additional high frequency pressure monitoring at the end of the diverter pumping. The combination of these methods may allow, for example, reliable determination whether a diverter works well, or if more diverter should be pumped. Moreover, the amount of viscous pill pumped may be reduced due to additional data received from the high frequency pressure monitoring. As a result, the treatment may be performed faster and with reduced cost. The higher accuracy of the diversion effectiveness achieved with the use of the two technologies may also allow restimulation of more stages (than with the use of viscous pill technology only) with a reduced (or even minimal) risk of understimulation of some stages and overstimulation of others.

According to the present embodiments, the refracturing operation is performed in a well, which has been previously stimulated and has a plurality of previously stimulated intervals, but in which hydrocarbon production dropped and thus a new stimulation (or restimulation or refracturing) is considered as feasible. In one or more embodiments, the refracturing operation is performed in a specific sequence of stages as described below. In such embodiments, a first stage of the stimulation treatment is to determine which of previously stimulated stages in the well are accepting fluids, followed by alternate stages of stimulation treatment (such as a hydraulic fracturing treatment) with the formation of new fracture(s) and isolation of such fracture(s) using diverters. The sequence of the steps is repeated until all stages planned for stimulation are stimulated (or earlier if design will be re-considered). Data may be collected and processed to evaluate the effectiveness of the stimulation treatment and to determine future stimulation treatments.

According to the present embodiments, the fluid used as a stimulation fluid can be of any type. It is also assumed that in some embodiments the properties of the fluid remain the same during the whole treatment process. It is also envisioned that in some embodiments the properties may change from one stimulation to another; in such embodiments, the difference may be taken into account by using correction coefficients on the tube waves velocity based on the fluid properties knowledge. In one or more embodiments, the properties of the fluid may be unknown or poorly determined. In such embodiments, a more viscous pill may be pumped.

According to one or more embodiments of the present disclosure, the refracturing operation of a well with multiple stages may include the following sequence of stages:

-   -   1. Pumping fluid according to a stimulation design to create a         first fracture. The fracture may appear in any of 1 . . . N         stages available in a well.     -   2. Isolating the created fracture by using a chemical         (dissoluble) diverter, i.e., a fluid with specially designed         particles, which may plug the opened fracture.     -   3. Pumping fluid according to the stimulation design to create a         second fracture. The second fracture may appear in any of 1 . .         . N stages available in a well. If a fracture is formed in a new         production stage, the stimulation is considered successful. If a         new fracture has not been formed and the fluid was pumped to a         first fracture, then the new stage is unstimulated, and         stimulation failed. The timely detected stimulation failure may         be used in order to update the stimulation schedule, for         example, to repeat the isolation step of already stimulated         stages, then change the concentration of additives in the         diverter pill, followed by adjusting the pill volume, then         making changes in the fracturing treatment design such as         adjusting the volume of a fluid pumped for fracture growth, or         adjusting the proppant/fibers concentration.     -   4. Isolating both of the existing fractures.     -   5. Performing a new stimulation treatment.

As noted above, the sequence of the steps is repeated until all stages planned for stimulation are stimulated (or earlier if design will be re-considered). The challenge is to predict whether the stimulation of a stage is successful, or if the fluid is pumped to already existing fractures. With the development of modeling, software, and hardware capacities, the ability to optimize designs before a treatment stage and in real-time has become more feasible. Currently, there are several methods of fluid entry point identification during refracturing, such as Distributed Temperature Sensing (DTS), Distributed Vibration Sensing (DVS), radioactive and chemical tracers, and microseismic technology. However, such approaches have numerous limitations and therefore the information provided has high measurement uncertainty that can limit the reliability of predictions.

DTS method involves pumping a large volume of cold fluid and long-term measurements of temperature distribution along the wellbore. DVS is very sensitive to a small volume of gases, as gas bubbles may cause false vibrations. The microseismic method works well only in mechanically solid formations and depends on the monitoring of well location vs. treated well. Moreover, the microseismic technology is not a near-wellbore method and is sensitive to events which occur few hundred feet away from the wellbore. Thus, the vertical depth in the wellbore is not accurately known. The presence of chemical or radioactive tracers shows rather high permeability zones of the formation, which may or may not relate to the fracture. Vice versa, the absence (or a concentration below the background) of chemical or radioactive tracers in the near well bore zone may mean that the particles were pumped deeply into the formation. At last, these methods are not popular due to HSE reasons.

Another method, which is widely used due to its simplicity and low cost is surface pressure monitoring. In such a case, the fluid entry point is not measured; instead, the diversion efficiency is monitored by the Instantaneous Shut in Pressure (ISIP) change method: the diversion is considered successful if the ISIP after stimulation exceeds ISIP after previous stimulation. Unfortunately, this method doesn't guarantee the accuracy of the results. In addition, the ISIP computation may take time and still may be determined with a certain degree of uncertainty. Thus, the difference between current and previous ISIPs should exceed a minimum threshold, which is subjective. Moreover, the negative difference between ISIPs doesn't mean poor diversion, the friction pressure losses should also be estimated: if it is increased from the previous stimulation, then the diversion is also successful regardless the ISIPs difference (friction pressure may be higher for formations with lower ISIP due to friction losses in the damaged near-wellbore zone).

Another method of fluid entry point identification is the viscous pill technology. When a viscous pill is pumped into a well an increase in pressure may be observed when the pill enters into the fracture. Using well completion data, pumping rate, and the time when fluid reaches fracture, the depth of fluid entry point may be predicted. However, in many cases this depth may be predicted with the accuracy comparable to the distance between stimulated stages and therefore may not give precise results. Moreover, pumping a viscous pill at the end of each stage may not be cost-effective and may involve a longer additional time. For these reasons, the viscous pill technology alone is not very widely used.

Without being bound by the theory, it was found by the present inventors that the drawback of using viscous pill technology may be overcome by combining such technology with high frequency pressure measurements. Such a combination may allow for monitoring the effectiveness of a refracturing treatment. In one or more embodiments, methods may utilize viscous pill technology, i.e., pumping of a viscous fluid (1000 and more cP at 100 s⁻¹ during at least 20 min with fast viscosity degradation down to 100 cP or less) and of high frequency pressure measurement with water hammers generation at the end of job and their further processing.

As described herein, high frequency pressure measurement is based on the analysis of water hammer signals (or tube waves) propagating in a wellbore. Tube waves are interface waves that occur in cased wellbores when a Rayleigh wave encounters a wellbore and perturbs the fluid in the wellbore. The tube wave travels down the wellbore along the interface between the fluid in the wellbore and the wall of the wellbore. Because the tube wave is coupled to the formation through which it is traveling, it can perturb the formation across open fractures intersecting the borehole, creating a squeezing effect that generates secondary tube waves that are reflected up and down from the fracture location. Intercepted secondary tube waves may contain signatures diagnostic of open fractures and their amplitude related qualitatively to the length and width, e.g., volume of the fluid-filled fracture space, in addition to other characteristics such as fracture closure pressure, fracture initiation pressure, and the like. Tube waves may also be used to detect other features such as obstructions, pipe sections of different diameters, perforations, and open fractures.

In practice, secondary tube waves may be deconvolved from primary tube waves by identifying the time and magnitude of the peak value of the envelope of the deconvolved signal. This time and magnitude will vary in a predictable manner, and the variation can be analyzed as a function of depth. Advanced algorithms for tube wave processing (e.g., cepstrum analysis as previously discussed) together with pressure source control mechanisms, including pump noise, active pulse sources, and the like, may also be used to extract date from tube waves to resolve positions of multiple fractures from a wellbore.

According to the present disclosure, high frequency pressure measurement may allow computing period of water hammers (or tube waves) generated at the end of each stage (or even between the stages, when the pumping rate changes very fast). These periods relate to the time required by tube waves for traveling from the wellhead to the fracture and being reflected from the fracture back. Periods (or reflection times) can be converted into the depths if the tube waves velocity is accurately known, which is not the common case. To predict this velocity, some other information may be involved for calibration. One of the methods is the use of a fluid entry point predicted by the viscous pill technology. In this case, a combination of time and depth provides a good estimation for the velocity (at least in a given stimulation stage). The reasonable assumption that the velocity doesn't change too much between the nearest stages, as well as the use of other methods as described later may give information on whether all of the stages are stimulated or not. The information may be obtained at the end of each stage and may be used by an operator to adjust stimulation design for further stages.

According to one or more embodiments, a method of treating a subterranean formation penetrated by a wellbore may include: a) pumping a viscous pill into a well with pressure curve registration by a wellhead pressure sensor; b) determining a depth (L) of treatment fluid entry point and depth uncertainties (ΔL); c) generating a water hammer at the wellhead which excites tube waves; d) determining the depth (L) of the treatment fluid entry point and the depth uncertainties (ΔL) by processing a water hammer by high frequency pressure monitoring method; e) determining a tube wave velocity from a combination of data from (b) to (d); f) performing a fracturing treatment and g) generating a water hammer at the wellhead at the end of the fracturing treatment (f) with refined depth of treatment fluid entry point and with lower uncertainty. In such embodiments, the well has a plurality of previously stimulated intervals. In one or more embodiments, multiple stimulation treatments may be pumped in the well.

According to one or more embodiments, the data frac (https://petrowiki.org/Glossary) treatment may be performed before pumping a viscous pill into the well. In such embodiments, the viscous pill may be a portion of fluid with a viscosity of at least 100 times higher than a viscosity of the wellbore fluid. In one or more embodiments, where multiple stimulation treatments are performed, the viscous pill is pumped before each fracturing treatment. In such embodiments, the water hammer may be generated by shutting down the pumps at the surface. In one or more embodiments, the high frequency pressure monitoring method involves processing a pressure signal, for example including preliminary signal filtering and further processing with cepstrum analysis. It is also envisioned that a diverter may be additionally pumped into the wellbore after stage (g). In such embodiments, the diverter may be a portion of particle slurry capable to isolate at least one of previously stimulated intervals. In one or more embodiments, the diverter may be selected from the group of chemical (dissoluble) and mechanical diverters.

In one or more embodiments, the method of treatment of a subterranean formation may further comprise performing a completion operation. In such embodiments, the completion operation is selected from the group of plug-and-perf completions or slide and sleeve completions.

It is also envisioned that the method of treating a subterranean formation penetrated by a wellbore may include 1) pumping a first viscous pill into a well located in the subterranean formation, where the well has a plurality of previously stimulated stages, 2) determining a depth (L) of treatment fluid entry point and a depth uncertainty (ΔL) for which of the previously stimulated stages are accepting fluid, 3) generating a water hammer at the wellhead to excite tube waves, 4) processing the water hammer by high frequency pressure monitoring method to determine the depth (L) of the treatment fluid entry point and the depth uncertainty (ΔL), 5) determining a tube wave velocity by combining 2)-4), 6) performing a first stimulation treatment (such as a fracturing treatment) in the at least one previously stimulated stage that is accepting fluid to form a first new fracture in the at least one previously stimulated stage, 7) generating a water hammer at the wellhead at the end of the fracturing treatment 6) with refined depth of the treatment fluid entry point and with lower uncertainty, 8) isolating the first new fracture by pumping a diverter, 9) computing at least a reflection time of water hammers and a reflection time uncertainty by using a high frequency pressure monitoring with water hammers generated at least at the end of one treatment stage, 10) predicting a tube wave velocity for the at least one previously stimulated (fractured) stage using at least the depth of fluid entry point (L) and the reflection time of water hammers, and 11) evaluating the effectiveness of the first stimulation treatment to determine future stimulation treatments, if any. In one or more embodiments, determining the depth (L) of fluid entry point and the depth uncertainty (ΔL) of the at least one previously stimulated stage is performed by viscous pill technology, high frequency pressure monitoring, or a combination thereof. In such embodiments, the depth (L) determination may have a resolution of at least 100 ft (30.48 m). In one or more embodiments, the maximum measured depth of at least a fracture may be up to 40000 ft (12192 m). It is also envisioned that multiple viscous pills and high frequency water hammers may be used during the first stimulation treatment stage.

It is also envisioned that a second viscous pill may be pumped into the well after isolating the first new fracture (achieved by pumping a diverter). The next stage is to verify whether the previously stimulated stages that are accepting fluid shift compared to an original value. If there is an indication that the first stimulation treatment was effective, and no additional amount of diverter is necessary, a second stimulation treatment at a second stage may be performed.

In such an embodiment, a second stimulation treatment in the at least a second previously stimulated stage that is accepting fluid to form a second new fracture is performed, followed by isolating the second new fracture by pumping a diverter, computing at least a reflection time of water hammers and a reflection time uncertainty by using a high frequency pressure monitoring with water hammers generated at least at the end of one treatment stage, predicting a tube wave velocity for the at least a second previously stimulated stage using at least the depth of fluid entry point and the reflection time of water hammers and evaluating the effectiveness of the second stimulation treatment to determine future stimulation treatments, if any.

It is also envisioned that when the first stimulation treatment is ineffective, an additional amount of diverter may be pumped. In such embodiments, the amount of the diverter may be adjusted (increased or decreased) based on the effectiveness of the refracturing. As described herein, the diverter may be selected from the group of chemical (dissoluble) and mechanical diverters. In such embodiments, a second isolation treatment on the at least one previously stimulated stage may be performed.

As noted above, the sequence of these treatment stages is repeated until all stages planned for stimulation are stimulated (or earlier if design will be re-considered). After the stimulation is performed, the next treatment stage is a completion operation. In such embodiments, the completion operation may be selected from the group of plug-and-perf completions or slide and sleeve completions.

It is also envisioned that the method of treating a subterranean formation is a method of stimulating a subterranean formation penetrated by a wellbore. In such illustrative embodiments, the method includes pumping a first viscous pill into a well located in the subterranean formation, where the well has a plurality of previously stimulated stages, performing a first stimulation treatment with the formation of a first new fracture in at least one previously stimulated stage that is accepting fluid, generating water hammer at the end of the fracturing treatment with refined depth of the treatment fluid entry point and with lower uncertainty and adjusting future stimulating treatment(s) according to processed input data collected during various treatment stages.

As noted above, the depth determination may have a resolution of at least 100 ft (30.48 m). In one or more embodiments, the maximum measured depth of at least a fracture is up to 40000 ft (12192 m).

According to one or more embodiments, multiple viscous pills and high frequency water hammers may be performed during a first stimulation treatment stage.

It is also envisioned that a second viscous pill may be pumped into the well after isolating the first new fracture by pumping a diverter. The next stage is to verify whether the previously stimulated stages that are accepting fluid shifted compared to an original value. If there is an indication that the first stimulation treatment was effective, and no additional amount of diverter is necessary, a second stimulation treatment at a second stage may be performed.

In such an embodiment, a second stimulation treatment in the at least a second previously stimulated stage that is accepting fluid to form a second new fracture is performed, generating water hammer at the end of the fracturing treatment with refined depth of the treatment fluid entry point and with lower uncertainty and adjusting future stimulating treatment(s) according to the processed input data collected during various treatment stages.

It is also envisioned that when the first stimulation treatment is ineffective, an additional amount of diverter may be pumped. As described herein, the diverter may be selected from the group of chemical (dissoluble) and mechanical diverters. In such embodiments, a second isolation treatment on the at least one previously stimulated stage may be performed.

As noted above, the sequence of these treatment stages is repeated until all stages planned for stimulation are stimulated (or earlier if design will be re-considered). After the stimulation is performed, the next treatment stage is a completion operation. In such embodiments, the completion operation may be selected from the group of plug-and-perf completions or slide and sleeve completions.

High Frequency Pressure Measurement

The use of a high frequency (at least 20 or 30 Hz) pressure measurement technology may allow obtaining much more information than the standard pressure metering. The fast flowrate changes from maximum to zero at the end of pumping may cause water hammers (or tube waves) to travel from the wellhead down to the fracture and back. The reflection time of these waves (typically, between 3 and 10 sec) may indicate the depth of the open fracture and generally may be used for the fluid entry point determination. These oscillations may contain other parameters besides the oscillation components, such as attenuation, pressure friction losses, fluid leakage to the formation, noise, or reflection from other elements in the wellbore. Thus, the reflection time may be difficult to be determined. However, various methods are developed for determining such parameters. For example, cepstrum analysis as represented below in FIG. 2, may be used for the reflection time measurement.

Referring now to FIGS. 1 and 2, FIG. 1 depicts a typical high frequency pressure curve during water hammer. Its cepstrogram is shown in FIG. 2. Specifically, FIG. 1 depicts a pressure oscillation at the end of pumping, while FIG. 2 depicts a cepstrogram, i.e. “amplitudes” of waves with different reflection time as a function of time. Referring to FIG. 2, 200 represents the strongest amplitude, i.e., main pressure wave reflections from the fracture, while 210, represented as a line, depicts the reflection time. The width of 210 determines its uncertainty.

In most cases, the tube wave velocity is unknown and reflection time itself is useless. Despite this, it may be possible to apply the special algorithm for velocity determination. In one or more embodiments, this can be described based on a plug and perf completion example, but it may be extended to all other cases. It is assumed that there are only N available stages, where the fractures can be potentially formed.

The depths of these stages are L₁ . . . L_(N), and the depth's uncertainty is σL₁ . . . σL_(N). In a normal case, when the stage has a width, ΔL_(i), the uncertainty, σ L_(i), can be computed as an uncertainty for the uniform distribution and is defined by formula 1:

$\begin{matrix} {{\sigma L}_{i} = {\frac{1}{2\sqrt{3}}{\Delta L}_{i}}} & (1) \end{matrix}$

The first fracture may be located at the first stage only (whose depth and depth uncertainty are known), as there are no other perforations. This allows the first stage velocity calculation and its associated uncertainty determination to be made. This data can be used as a first guess for the second stage velocity calculation, which combined with the reflection time of the events (such as water hammers) after the second stage treatment, may predict the possible depth of the second stage's fracture. Further, this predicted depth is compared with the perforation depth of the second stage (if the mechanical isolation is successful) and perforation depth of the first stage (if the mechanical isolation is a failure/leak). The difference between the predicted depth and available stage's depth cannot exceed two to three sigma values, where sigma is a standard deviation (or uncertainty) of the difference, which can also be computed. This allows for prediction of whether or not the second stimulation was successful, and it may provide a probability of the successful stimulation if both scenarios occur.

Moreover, for each of these scenarios, the velocity may be defined with higher accuracy when information from more than one stage is available, for example data from the first and second stage pumping operations. A similar principle may be used for subsequent events (stimulations). Some advanced statistical methods (including Bayesian techniques) may allow for the prediction of each treatment fracture location considering each available scenario more precisely as more measurements are recorded, tuning velocity value and its slow change along the lateral.

At any stage, more than one scenario may exist, but all of them have their own probability p, which are based on the maximum likelihood method as described by formula 2:

$\begin{matrix} {{\left. {p\left( {{i1},{i2},{\ldots\mspace{14mu}{in}}} \right)} \right.\sim{\exp\left( {- \frac{\left( {D_{1} - L_{i1}} \right)^{2}}{2\left( {{\sigma D}_{1}^{2} + {\sigma L}_{i1}^{2}} \right)}} \right)}}*{\exp\left( {- \frac{\left( {D_{2} - L_{i2}} \right)^{2}}{2\left( {{\sigma D}_{2}^{2} + {\sigma L}_{i2}^{2}} \right)}} \right)}\mspace{14mu}\ldots\mspace{14mu}{\exp\left( {- \frac{\left( {D_{n} - L_{in}} \right)^{2}}{2\left( {{\sigma D}_{n}^{2} + {\sigma L}_{in}^{2}} \right)}} \right)}} & (2) \end{matrix}$

Finally, the number of possible scenarios may be very large if the data for each event is very inaccurate (high values of στ_(i) and σL_(i)—reflection time and depth uncertainties) and/or there are only few events. Vice versa, this number may be small (just a few, or even one) if the reflection times are determined accurately and the stage width is small compared to the distance between them and the total number of stimulations is high enough.

Viscous Pill Technology and High Frequency Pressure Measurements

According to the present embodiments, viscous pill technology and high frequency measurements may be used together. Such a combination may allow performing the refracturing monitoring faster, with a high level of confidence, in a short time and with minimum resources. In such embodiments, the monitoring is performed as follows:

-   -   1. Pump a viscous pill and determine a fluid entry point with         uncertainty. Assign this fluid entry point to one of few stages         with their own probabilities. The number of possible scenarios,         where the fracture will be created is less or equal to the total         number of stages.     -   2. Perform the first stimulation treatment. Using water hammers         at the end of the treatment stage may allow for determination of         the reflection time and uncertainty. Using the depths of         possible stages and the reflection time obtained may predict         velocity for each of the stages determined above at point 1.     -   3. Pump diverter. At the end of the diverter pumping use water         hammers to receive a new reflection time which combined with the         velocity for each of the possible scenarios may predict a new         depth. This is further compared with all the possible stage         depths where the second fracture may go.     -   4. Generate a new set of scenarios with their probabilities,         which are proportional to the product of probabilities from         points 1 and 3 above. After normalization, the scenarios with         probabilities less than a predefined threshold (for example 0.5%         or 0.01 of the most probable scenario) may be removed from the         consideration.     -   5. If the number of scenarios is more than one, depending on         their relative probabilities, time and resources restrictions,         the new diverter may be pumped or not.     -   6. Perform the second stimulation. Using water hammer at the end         of a treatment stage may determine reflection time and         uncertainty. Using the data of all existing scenarios, compare         the predicted depth of the second fracture shown in formula 3

$\begin{matrix} \frac{v_{2}\tau_{2}}{2} & (3) \end{matrix}$

with all possible stages to evaluate where it may be located (here velocity and reflection time are used, coefficient ½ comes from the travel path: wellhead-bottomhole and back). If the location of a fracture differs from the location of a previous fracture, the stimulation may be considered as successful and the velocity may be updated using all data available as should be similar and, for example, the real velocity at each stage may be computed as described in formula 4:

$\begin{matrix} {{v_{n} = \frac{2{\sum_{i = 1}^{N}{w_{i}D_{i}\tau_{i}}}}{\sum_{i = 1}^{N}{w_{i}\tau_{i}^{2}}}},} & (4) \end{matrix}$

where τ_(i)—reflection time of i-th event, D_(i) is the calculated depths of a fracture, corresponding to this event, weights w_(i) represent weights of events (the higher event reflection time and depth uncertainty, the smaller its weight). The new probability for all scenarios is computed as a normalized product of probabilities determined at 1, 3, 5, 6. However, it is not the common case that only one scenario remains at this stage even if the stimulation is evaluated as successful. In fact, there might be few scenarios if in each of them the first stage differs from the second stage. If the stimulation failed in some of the scenarios, the probability of failure should be evaluated as described by formula 5:

1−Σ_(i=1) ^(N) p _(i)*(1 if successful divertion)  (5)

If the probability of failure is high enough, further actions may be performed, such as a new event generation (start and stop injection, open or close valve, etc.). For example, in such a case, its water hammer may be analyzed, and used in all re-evaluation scenarios. If the probability failure is still high, further actions such as new viscous pill pumping, its depth evaluation, scenarios re-evaluation, etc. may be performed. If the failure is still probable, pumping an additional diverter may be performed.

-   -   7. Pump a new diverter. Re-evaluate all scenarios.     -   8. Perform a third stimulation treatment. Using water hammer at         the end of the treatment stage may allow for determination of         reflection time and uncertainty. Using the data, re-evaluate all         scenarios to make a solution on the stimulation efficiency of         all three stimulations.     -   9. Continue the stimulation treatment.

This flow chart of on-site decision making is shown in FIG. 3. Such a flow chart may allow for performing a refracturing operation in a well having multiple stimulation stages much faster than with currently used methods, with reduced resources, while providing more reliable information regarding the effectiveness of the stimulation treatment for each stage.

Examples

The following examples are presented to further illustrate the refracturing monitoring method in accordance with the present disclosure and should not be construed to limit the scope of the disclosure, unless otherwise expressly indicated in the appended claims.

For comparative purposes, a classic viscous pill technology was used. The classic viscous pill technology (without high frequency pressure monitoring) involves the following sequence of stages:

-   -   1. Mixing the pill with the use of a linear gel and a         crosslinking agent.     -   2. Pumping approximately 3-4 m³ of the viscous pill (with the         viscosity at least 100 times higher than the viscosity of         wellbore fluid) at a low flowrate. The first viscous pill is         pumped into a well following the injection test. Such a pill is         used to identify the most fluid-accepting stage. Identification         is done by the pressure monitoring and analysis. The surface         pressure slope should increase at the point when a viscous pill         enters a fracture.     -   3. Performing a first stimulation stage.     -   4. Pumping a diverter (isolation agent) into the wellbore.     -   5. Pumping a second viscous pill to verify whether the fluid         accepting point shifted compared to the original value (position         of diverter isolation action). Depending on the result (if         diverter fails), the additional amount of chemical (dissoluble)         diverter may be pumped, or other actions can be done in         agreement with the client.     -   6. When the diversion is achieved, the second stimulation         (fracturing) is performed, and the treatment continues the same         way from one stimulation stage to another.

The method of fluid entry point determination may assume the search of an optimal point of intersection of two (almost) linear parts of the pressure-time curve with its statistical processing. This point of intersection combined with the wellbore completion data and pumping rate provides fluid entry point depth. The stage that accepts fluid is predicted by comparison with the depths of various stages.

A typical pressure curve with the analysis of fluid entry point determination is shown in FIG. 4. Referring to FIG. 4, FIG. 4 depicts the identification or marker pill as described in WO Publication No. 2018/004370. As seen in FIG. 4, a slope change from a small inclination to a high one determines the time of viscous pill entering the open fracture (since the pumping starts). The result gives 17.7+/−0.3 min. For the typical velocity of a pill travel in a liner ˜2 m/s, this causes the error in depth estimation about 36 m, which is comparable with the typical distance between stages. Thus, the viscous pill positioning with this accuracy doesn't guarantee a reliable answer for all treatment stages.

A two-stages of re-fracturing was performed in a well. The well itself contains 4 stages (perforations separated by packers). The first stimulation was performed as a data frac in order to obtain general formation properties (pressure decline curve analysis) and determine which stage is the most accepting fluid (with the use of high frequency pressure monitoring). The data frac (or pre-frac) operation is defined as a pumping of moderate amount of clean fracturing fluid at the pressure above the reservoir fracturing pressure for gathering of information about the mechanical properties of rock—this evaluation is needed for more accurate predicting of later full-scale fracturing operation (herein—stimulation). Since information about the tube wave velocities (except physical restrictions for wellbore fluid from 1300 m/s to 1700 m/s) was lacking, this measurement was not conclusive, and a viscous pill was further involved. After that, three sets of data were available: data frac (processed using HFPM), viscous pill depth determined by the pressure sharp increase (standard viscous pill technology) and water hammer at the end of the viscos pill (processed with HFPM technology). The results are shown in Table 1.

It is observed that the use of a viscous pill only predicts stages with the probabilities of 28 and 72% for the stages 3 and 4. If the viscous pill pumping is the only technology used, the operator cannot rely on this data. In a given case, the HFPM technology was also applied and predicted 30 and 70% for the same stages in the wellbore. Thus, their combination (combination of probabilities from different kinds of measurements) is more reliable. The main treatment stage gives one more piece of information (water hammer at the end of pumping, which is processed with HFPM); the results of three pumping operations are shown in Table 2. It is worth noting that the water hammer data even in combination with all the previous data is not conclusive for identification of the dominant fluid-accepting stage: most likely stage 4 is accepting the fluid (with a lower probability of 3^(rd) stage). It may mean that both stages are accepting the fluid simultaneously at different flowrates.

When the chemical (dissoluble) diverter (isolation agent) is pumped, the produced water hammer date are analyzed and they show that the previous stages (3 and 4) are isolated (Table 3). This information is already enough to perform the second stimulation, and as a result, viscous pill pumping is not performed at this stage. However, the water hammer quality after diversion pumping is in general poor. This is because during diversion pumping the most fluid-accepting stages are isolated (blocked), and the tube wave reflections may exist only from minor contributors (i.e., almost closed fractures, which did not accept the fluid).

TABLE 1 Refract Monitoring results with the use of HFPM and VP technologies. Two fluid injections are done (data frac and viscous pill) Stimulated (fractured) stages OPERATION 1 2 3 4 DataFrac1 (HFPM 0% 11% 59% 30% processing) Viscous Pill 1 (HFPM 0% 0% 30% 70% processing) Viscous Pill 1 (VP) 0% 0% 28% 72%

TABLE 2 Refracturing Monitoring results with the use of HFPM and VP technologies. Main job (fracturing) is added. Stimulated (fractured) stages OPERATION 1 2 3 4 DataFrac1 (HFPM 0% 11% 59% 30% processing) DataFrac1 (HFPM processing) 0%  0% 30% 70% Viscous Pill 1 (HFPM 0%  0% 28% 72% processing) Main frac job 1 (HFPM 0%  0% 42% 58% processing)

TABLE 3 Refracturing Monitoring results after pumping a chemical (dissoluble) diverter. Stimulated (fractured) stages OPERATION 1 2 3 4 DataFrac1 (HFPM processing)  0% 11% 59% 30% DataFrac1 (HFPM processing)  0%  0% 30% 70% Viscous Pill 1 (VP)  0%  0% 28% 72% Main frac job 1 (HFPM  0%  0% 42% 58% processing) Diverter pumping (HFPM 71% 24%  4%  0% processing)

Next, the second main treatment stage may be pumped. The results are shown in Table 4 below. In such a stage, the viscous pill is pumped. Table 5 presents the results for this pumping stage. However, the viscous pill may not be performed due to the combined use of VP and HFPM technologies in the previous stage stimulation. The results seen in Table 5 are identical with the results obtained without the second viscous pill pumping. This may allow saving time and resources and may allow for starting the oil production at a specific well faster. In this case, two major treatment stages were analyzed. If there are more than two consecutive stimulation treatments, evaluation of time and resources needed may to be taken into consideration.

The results may be represented as shown in FIGS. 5 and 6. Referring now to FIGS. 5 and 6, FIGS. 5 and 6 represent the depth of fluid entry point for all events. The cloud size determines the depth uncertainty; more than one cloud per event shows probability of different stages stimulation. As seen for example in FIG. 5, the clouds are located at the calculated depths, their sizes indicate depth's uncertainties (in this figure only the final results are shown). It is easy to see the stimulation depth change over the whole treatment: the data frac, first viscous pill pumping, and major treatment stage (job 1) show the stimulation with the stages 3 and 4. The diverter analysis showed that most likely the stages 3 and 4 are plugged and there is a reflection from the stages 1; further measurements fully confirm that.

TABLE 4 Refrac Monitoring results without a second viscous pill. Stimulated (fractured) stages OPERATION 1 2 3 4 DataFrac1 (HFPM processing)  0% 11% 59% 30% Viscous Pill 1 (HFPM processing)  0%  0% 30% 70% Viscous Pill 1 (VP)  0%  0% 28% 72% Main frac job 1 (HFPM  0%  0% 42% 58% processing) Diverter pumping (HFPM  71% 24%  4%  0% processing) Main frac job 2 (HFPM 100%  0%  0%  0% processing)

TABLE 5 Refrac Monitoring results with the second viscous pill. Stimulated (fractured) stages OPERATION 1 2 3 4 DataFrac1 (HFPM processing)  0% 11% 59% 30% Viscous Pill 1 (HFPM processing)  0%  0% 30% 70% Viscous Pill 1 (VP)  0%  0% 28% 72% Main frac job 1 (HFPM processing)  0%  0% 42% 58% Diverter pumping (HFPM  71% 24%  4%  0% processing) Viscous Pill 2 (HFPM processing) 100%  0%  0%  0% Viscous Pill 2 (VP) 100%  0%  0%  0% Main frac job 2 (HFPM processing) 100%  0%  0%  0%

Advantageously, embodiments of the present disclosure provide refracturing monitoring methods that allow determining the effectiveness of refracturing a subterranean formation. Specifically, it was found that such methods may allow determination of the depth of a stage accepting fluids based on the pressure response of a viscous pill combined with high frequency pressure monitoring. The method provides features such as pressure wave velocity calibration, insurance in fluid entry point, measurement of depths of stimulated stages and avoidance of overstimulating already stimulated stages. The method as described herein may be applied for any fracture sizes, as well as any distance between fractures. In addition, the refracturing effectiveness monitoring method as described herein may provide on the fly calibration of pressure wave velocity.

Although only a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from this invention. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims. In the claims, means-plus-function clauses are intended to cover the structures described herein as performing the recited function and not only structural equivalents, but also equivalent structures. Thus, although a nail and a screw may not be structural equivalents in that a nail employs a cylindrical surface to secure wooden parts together, whereas a screw employs a helical surface, in the environment of fastening wooden parts, a nail and a screw may be equivalent structures. It is the express intention of the applicant not to invoke 35 U.S.C. § 112, paragraph 6 for any limitations of any of the claims herein, except for those in which the claim expressly uses the words ‘means for’ together with an associated function. 

1. A method of treatment of a subterranean formation penetrated by a wellbore, wherein the well has a plurality of previously stimulated intervals comprising: a) pumping a viscous pill into a well with pressure curve registration by a wellhead pressure sensor; b) determining a depth (L) of treatment fluid entry point and depth uncertainties (ΔL); c) generating a water hammer at the wellhead which excites tube waves; d) determining the depth (L) of the treatment fluid entry point and the depth uncertainties (ΔL) by processing a water hammer by high frequency pressure monitoring method; e) determining a tube wave velocity from a combination of data from (b) to (d); f) performing a fracturing treatment; and g) generating a water hammer at the wellhead at the end of the fracturing treatment (f) with refined depth of treatment fluid entry point and with lower uncertainty.
 2. The method of claim 1, wherein multiple stimulation treatments are pumped in the well.
 3. The method of claim 1, wherein the data frac treatment is performed before pumping a viscous pill.
 4. The method of claim 1, wherein the viscous pill is a portion of fluid with a viscosity of at least 100 times higher than a viscosity of a wellbore fluid.
 5. (canceled)
 6. The method of claim 1, wherein the water hammer is generated by shutdown of pumps at the surface.
 7. The method of claim 1, wherein the high frequency pressure monitoring method comprises processing of a pressure signal.
 8. The method of claim 7, wherein processing of the pressure signal comprises preliminary signal filtering.
 9. The method of claim 7, wherein processing of the pressure signal further comprises processing with cepstrum analysis.
 10. The method of claim 1, wherein a diverter is additionally pumped into the wellbore after (g).
 11. (canceled)
 12. (canceled)
 13. The method of claim 1, wherein the depth determination (L) has a resolution of at least 100 ft (30.48 m).
 14. (canceled)
 15. The method of claim 1, further comprising performing a completion operation, wherein the completion operation is selected from the group of plug-and-perf completions or slide and sleeve completions. 